Mustafa Qamar-ud-Din

 

Introduction

 Today, computer algorithms are present in every aspect of our daily lives without us noticing their existence. The smart phone in one’s pocket is thousands of times more powerful than the computer NASA used to ensure the first human landed on the moon. In 1982 a new paradigm in computing – quantum computing – was set forth by physicist and Nobel Prize-winner Richard Feynman. Quantum computing makes use of the laws and principles of Einsteinian quantum physics to perform unprecedented numbers of calculations in parallel. Together we shall examine how quantum computing influences the finance sector and the implications of the new interdisciplinary research field of quantum finance.

 

Computational Intractability

Computational complexity theory is a cornerstone of today’s computer science. Without jumping into mathematical jargon, there is a family of problems that are intractable to digital computers. This is a major problem that remains unsolved till now. The person who can correctly solve this puzzle is entitled to a prize of $US 1 million from the Clay Institute.

 

Quantum Superposition

Quantum computers exhibit an inherent parallelism, allowing them to solve an exponential number of problems simultaneously. How is that possible? The answer comes from the Schrödinger’s Cat thought experiment. This experiment examines the superposition of two states at a microscopic level and how each influences the cat at a macroscopic level. A microscopic object such as an atom, an electron, a muon, or a photon can exist in multiple states at the same time in what is known as quantum superposition. This allows a quantum computer to solve multiple problems at the same time, although only the final state is observed to collect the results.

 

Quantum Finance

 The finance sector has been one of the very earliest adopters of digital computers. However  many intractable problems remain, waiting to be solved by mathematicians, programmers and economists. Any possible existing solutions will take years for digital computers to solve. Scientists from different fields including finance, computer science, quantum computing, and quantum mechanics have come together to address these problems. Hence, the term quantum finance was coined for this new interdisciplinary field.

 

Quantum Finance Applications

 Classic computers have empowered economists with technological tools. These tools range from basic spreadsheet application to complex enterprise resource planning solutions. The finance sector has benefitted substantially from such advanced computational power. These tools have assisted in addressing problems related to financial modeling, complex analysis, estimating the time value of money, cash flow analysis, loan repayments, interest rates, asset valuation, future growth forecasting and business process workflow modeling.

In a fast paced economy, even this has not been good enough to match the unbounded ambition of decision makers. Some problems are still intractable, including optimal trading trajectory, multi-period profile optimization, risk management, regression analysis, scenario analysis and path-dependent option pricing. Herein lies the value of using quantum computing to solve intractable financial problems. Finding scalable solutions to these problems empowers decision makers with insight and analytics. These problems were previously deemed to require years of analysis to solve, but with the advent of quantum algorithms they can be solved in a matter of days, if not less.

 

The Flash Crash

If we take, for example, the “Flash Crash” crisis of 2010 in the United States, a sudden crash of the American stock market lasting approximately 36 minutes that caused the loss of over $US 1 trillion, economists spent more than five months analyzing the problem to find out the real reasons behind the crash. It was postulated that the most likely causes were US Dollar – Japanese Yen exchange rates, fat-finger trade of Procter & Gamble stock, or a large purchase of put options by the hedge fund “Universal Investment”. However, the final report blamed a small-time day-trader for the crash.

Five years later, a study conducted by Easley et al. proved that high-frequency trading (HFT) made the modern US economy subject to such incidents. HFT is a set of complex computer algorithms that are characterised by the automated buy/sell decisions they make after investigating investment horizons. Such horizons are not adequate to ensure arrival at the optimal decisions, since high frequency traders compete over making faster decisions within fractions of milliseconds and taking advantage of slower traders.

For example, any asset manager willing to invest a certain amount has to first study his investment on a horizon divided into multiple profiles. At each step, he must consider the associated risk, the price impact and the transaction cost. This could be modeled as a maximization problem for the expected return, resulting in a series of statistically optimal portfolios. As a consequence, a portfolio rebalance is executed at every step, so asset managers frequently perform portfolio rebalances frequently, exposing investors to a loss of funds due to transaction costs and price impact.

Classic computers use heuristics to arrive at conclusions because they don’t have the computational power to discover every possible path. The automated decision making process may take a few milliseconds or several seconds, with such a disparity known as latency. In an environment where HFT competition is very fierce, the delay of even one millisecond could translate into the loss of millions of dollars. HFT is blamed for such tremendous incidents, but the hope is that as algorithms mature and high frequency traders fine-tune their performance, traders shall be able to keep competing and the environment shall auto-correct and regain balance.

Quantum finance carries within its folds the very solution to such repeated HFT crashes. Meanwhile, several other theories for the real causes of the crisis have been postulated and an interested reader is advised to get acquainted with terms such as jitter. It’s worth noting that the 2010 Flash Crash is ranked as one of the top three financial crises caused by HFT. Look up Peet’s Coffee & Tea and Knight Capital to learn more about similar incidents caused by HFT and their related analyses.

 

Quantum Annealing

 D-Wave Systems is a Canadian venture which built a special purpose quantum computer to perform quantum annealing. Google, NASA and other tech pioneers are the major clients for this quantum annealer, with D-Wave having recently announced the release of a 2000 qubits quantum annealer. Qubits are the building blocks of a quantum computer. The new release, which was announced in January 2017, is called 2000Q and is a major breakthrough, as D-Wave has doubled the number of qubits from that of the previous chip (1000Q).

A quantum annealer is not a general purpose quantum computer – meaning that it cannot solve all kinds of computational problems, as special purpose computers solve only a defined set of problems. Quantum annealers however solve the optimization problem, which is the underlying core of the well-known intractable problems in machine learning, radiotherapy and financial analysis. Financial service companies have shown great interest in 2000Q, as they hope to get their hands on this cutting-edge technology. Even though 2000 qubits may sound like a large number, the chief scientists of quantum computing believe that millions of qubits are needed to create quantum annealers of adequate commercial interest. However, this number is unlikely to be realized in the foreseeable future.

D-Wave targets applications of quantum computing in outer space, while VC backed Rigetti and Microsoft have different approaches to quantum computing which shall be discussed in a dedicated technical review of the subject.

 

Closing Thoughts

Key players in the financial sector should be acquainted with quantum finance and the potential it offers them. Just as digital computers have changed our modern economy, quantum computers seem set to be a disruptive technological force that will affect the finance sector and subsequently all the rules of the game. A knowledge of quantum finance will inevitably be a must-have qualification for tomorrow’s economists.

 

 

Mustafa Qamar-ud-Din is an entrepreneur who specializes in the use of computer technology to solve real-world social challenges. Find out more about his work by visiting the website of his start-up, mQubits: http://mqubits.com

 

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